7.3 Spatio-temporal correlations with
7.5.1 Loop-shaped structures
In this section the significance of the stream-wise vortices for the turbulent mixing in wall-bounded flows will be examined and the existence of the loop-shaped structures, highlighted on page 6 will be validated. Loop-shaped structures can be best detected in the ¹Ã -plane of a turbulent boundary layer (wall-normal span-wise) because these structures are inclined in stream-wise direction [13, 28, 49]. Their footprint is a counter-rotating vortex pair with a strong velocity component being normal to the wall between the vortex pair as indicated in figure 1.3. In planes which are parallel to the wall (stream-wise span-wise) these loops appear as counter-rotating vortices with a typical out-of-plane motion between the vortex cores as illustrated in section 6.4. Thus the basic turbulent mixing process associated with this hairpin vortex is the transfer of low-speed fluid from the wall and high speed fluid towards the wall such that /. äã becomes positive on average. Since the early flow visualisation experiments performed in a laminar boundary layer, it is generally accepted that looped shaped structures result from a progressive deformation of a span-wise vortex with an initial three dimensional disturbance, as shown in the lower figure on page 6. The inclination of the vortices on the other hand is explained by means of self-induction of the developing vortex loop, and the stretching is assumed to be a result of the strong velocity gradients present in boundary layer flows [31].
However, it is still a point of discussion if these loop-shape structures are the predominant coherent velocity regions in turbulent boundary layers which are mainly responsible for the turbulent mixing. In the past, many attempts have been made in order to validate the existence and significance of these structures. The continuing discussion implies that no convincing experimental or theoretical evidence could be presented. As the signature of these coherent structures is a counter-rotating vortex pair with a strong velocity component normal to the wall between the vortex pair, as indicated in figure 1.3, they can be easily identified when the measurement plane is perpendicular to the wall and mean flow direction. Figure 7.18 shows two independent velocity fields where many well developed vortex pairs can be observed in
7 Investigation of the yz-plane
the near-wall region below¹&» Û ¿ (see circles). Moreover it can be seen that these vortices induce a wall-normal velocity as indicated in figure 1.3. This is fully consistent with the results discussed in section 7.2.2. In addition the red contours, which represent a negative out-of plane velocity fluctuation (ä Û ), show that the stream-wise velocity of the fluid between the vortex pairs is relatively low with respect to the mean motion. This implies that turbulence is produced by these structures as expected and discussed in the previous chapters. The blue contours indicate that the structures are frequently flanked by high-speed fluid.
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FIGURE7.18: Velocity fluctuations (blue: 021Á ; red: 023~ ) with loop shaped structures, see circles.
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7.5 Properties of coherent velocity structures
7.5.2 Sweeps
In order to interprete the results from the previous chapter it was assumed that the lifting of low-speed fluid from the wall is mainly caused by the high-momentum flow structures which move towards the wall. This interaction is shown exemplary in figure 7.19. Clearly visible is the strong wall-ward motion of a large-scale high-momentum flow structure in the lower image and the generation of looped shaped structures similar to those shown in the previous figure. The upper figure reveals similar structures but it should be noted that the
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FIGURE7.19: Same as figure 7.18 but with strong sweeps (041~ and563~ ).
7 Investigation of the yz-plane
span-wise size of the high-speed flow structures, which reach the wall, is quite small with respect to the structure visible in the lower image. To examine structures which contribute to the turbulent mixing to a large extent, the Reynolds shear stress component was calculated for each sample field and afterwards analysed if the intensity of this quantity was below a given threshold of S (Â . It was already mentioned that the dominant structures with regard to the magnitude of the Reynolds shear stress component appear quite seldom and do not contribute to the total production of turbulence to a large extent. However, as the structural features are
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FIGURE7.20: Same as figure 7.18 but with strong production of turbulence (07583~ ).
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7.5 Properties of coherent velocity structures assumed to be universal and thus independent on the magnitude of/. äã , it is evident that their geometrical and dynamical properties can be best examined when the effect of the background turbulence, which often deteriorates the analysis of the less intense structures, becomes small in relation to the structures under investigation. Figure 7.20 shows two samples measured independently at ª«¶_¬ ®w¯ . Clearly visible in both velocity fields is the high-momentum large-scale motion (blue), which moves towards the wall, and the effect when these structures interact in the near-wall region with the low-momentum structures (red).
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FIGURE7.21: Same as figure 7.18 but measured simultaneously at spatially separated planes (É ¨ »
Î ) to examine the length of the stream-wise vortices in¨ -direction.
7 Investigation of the yz-plane